# saturated

Let $S$ be multiplicative subset of $A$. We say that $S$ is a *saturated ^{}* if

$$ab\in S\Rightarrow a,b\in S.$$ |

When $A$ is an integral domain^{}, then $S$ is saturated if and only if its complement $A\backslash S$ is union of prime ideals^{}.

Title | saturated |
---|---|

Canonical name | Saturated |

Date of creation | 2013-03-22 12:30:17 |

Last modified on | 2013-03-22 12:30:17 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 4 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 16U20 |

Related topic | MultiplicativeSet |

Related topic | Ideal |

Related topic | PrimeIdeal |

Related topic | IntegralDomain |

Related topic | Ring |